A triangle has corners at #(1 ,9 )#, #(-6 ,-1 )#, and #(1 ,-2 )#. If the triangle is dilated by a factor of #2 # about point #(-5 ,-2 ), how far will its centroid move?
1 Answer
Explanation:
If all vertices of a triangle are dilated by a factor
Let
Let
Centroid of
The coordinates of the centroid can be found by taking the arithmetic mean of the x coordinates and the y coordinates.
Using vectors:
Position vector of centre of dilation:
Let
Vector from D to C:
Scale factor = 2:
Position vector of new centroid
Distance the centroid has moved can be found using the distance formula: